The problem however becomes more tractable for certain non-compact CY threefolds, such that the category \(D^b\operatorname{Coh}(\mathfrak {Y})\)  is isomorphic to the derived category \(D^b\operatorname{Rep}(Q,W)\)  of representations of a certain quiver with potential \((Q,W)\) . In particular, in the vicinity of an orbifold point where the central charges associated to the nodes of the quiver all lie in a common half-plane, the heart of the stability condition reduces to the category of quiver representations (or some tilt of it) and
the notion of attractor index has a simple definition using
King stability for the (suitably perturbed) `self-stability' parameter
\(\theta _\star (\gamma )=\langle -, \gamma \rangle \)  [1]}. In that context, the enumeration of attractor flow trees becomes straightforward and precise versions of the Split Attractor Flow Conjecture
have been
proposed [2]}, [1]} and then established rigorously [4]}, [5]} using the mathematical framework of operads and scattering diagrams, respectively. As already anticipated in [6]} and as
will become apparent shortly, scattering diagrams turn out to
be the mathematical incarnation of split attractor flows (at least for non-compact CY threefolds), while the physical interpretation of the trees in the operadic approach of [4]} remains obscure at present.
